1. Field of the Invention
The present invention relates to force balancing of a Coriolis flow meter.
2. Statement of the Problem
Vibrating flow tube sensors, such as Coriolis mass flow meters, typically operate by detecting motion of a vibrating flow tube (or tubes) that contains a material. Properties associated with the material in the flow tube, such as mass flow and density may be determined by processing signals from motion transducers associated with the flow tube. The vibration modes of the vibrating material-filled system generally are affected by the combined mass, stiffness and damping characteristics of the containing flow tube and the material contained therein.
A typical Coriolis mass flow meter may include two flow tubes that are connected inline with a pipeline or other transport system and convey material, e.g., fluids, slurries and the like, in the system. Each flow tube may be viewed as having a set of natural vibration modes including, for example, simple bending, torsional, radial and coupled modes. In a typical Coriolis mass flow measurement application, two U-shaped flow tubes that are oriented parallel to each other are excited to vibrate about their end nodes in the first out-of-phase bending mode. End nodes at the ends of each tube define each tube's bending axis. A plane of symmetry exists half way between the flow tubes. In the most common mode of vibration, the flow tubes' motion is a periodic bending toward and away from each other about the plane of symmetry. Excitation is typically provided by an actuator, e.g., an electromechanical device, such as a voice coil-type driver, that pushes the flow tubes in a periodic fashion in phase opposition at the tubes' resonant frequency.
As a material flows through the vibrating flow tubes, the motion of the flow tubes is measured by motion transducers (commonly called pick-off transducers) at points spaced along the flow tube. Mass flow rate may be determined by measuring time delay or phase differences between motion at the pick-off transducer locations. The magnitude of the measured time delay is very small; often measured in nanoseconds. Therefore, it is necessary that the pick-off transducer output be very accurate.
Coriolis mass flow meter accuracy may be compromised by nonlinearities and asymmetries in the meter structure or from undesired motion arising from extraneous forces. For example, a Coriolis mass flow meter having unbalanced components can cause external vibration of its case and of the attached pipeline at the drive frequency of the meter. The coupling between the desired flow tube vibration and the undesired external vibration of the entire meter means that damping of the meter's external vibration damps the flow tube vibration, and that a stiff meter mount raises flow tube frequency while a soft meter mount lowers flow tube frequency. The change in flow tube frequency with mounting stiffness has been observed experimentally in meters with high external vibration amplitude. It is a problem because flow tube frequency is used to determine fluid density. Frequency is also an indication of flow tube stiffness. Changes in flow tube stiffness due to mounting stiffness change the calibration factor of the meter. The direct coupling between the drive vibration and (via external vibration) the local environment also results in an unstable zero signal (a flow signal when no flow is present).
The undesired external vibration perturbs the meter output signal in an amount that depends on the rigidity and damping of the mount. Since the characteristics of the mount are generally unknown and can change over time and temperature, the effects of the unbalanced components cannot be compensated and may significantly affect meter performance. The effects of these unbalanced vibrations and mounting variations are reduced by using flow meter designs that are balanced.
The balanced vibration mentioned above traditionally involves only a single direction of vibration: the Z-direction. The Z-direction is the direction that the flow tubes are displaced as they vibrate in phase opposition. This is often called the drive direction. Other directions may include the X-direction along the pipeline and the Y-direction perpendicular to the Z and X-directions. This reference coordinate system is important and will be repeatedly referred to.
There are also secondary sources of unwanted vibration in the Y-direction resulting from tube geometry. The tube geometry is normally configured so that the motion of the tubes' centers of mass is toward. and away from each other about the plane of symmetry. Thus the momentum of the oscillation of the tube (and fluid) masses largely cancels. In order to avoid Y-motion of the tube centers of mass, each center of mass must lie on its respective plane that includes its bending axis and is parallel to the symmetry plane. These planes will be referred to as the balance planes. If the symmetry plane is vertical, the centers of mass must lie directly above the bending axes to insure that this Y-direction vibration cancels.
There is also a secondary vibrating force in the Y-direction resulting from the driver, pickoff transducers, and other masses attached to the vibrating portion of the flow tubes. The sum of these additional vibrating components will be referred to, for simplicity, as the vibrating components. If the center of mass of the vibrating components attached to each flow tube is offset from that tube's balance plane, a Y-direction vibrating force is generated. This is because the tubes' bending motion has a rotation component. If the driver mass is offset from balance plane in the Z-direction, then the rotational component of tube motion causes the driver mass to have a component of motion in the Y-direction. The source of the Y-direction motion can be understood by visualizing an extreme offset of a mass. If a mass is offset from the balance plane by a 45 degree angle (taken from the bending axis), then the rotational component of motion causes it to move equally in the Y and Z-directions as it vibrates. Equal offset masses on the two vibrating tubes balance the forces in the Z-direction but not in the Y-direction.
EP 1 248 084 A1 discloses a solution to the problems of Y-vibrations by affixing an offset mass to the opposite side of a flow tube as the driver mass so as to bring the combined center of mass onto the flow tube's balance plane plane.
Secondary unbalanced vibration forces can also be generated in the Z-direction even when the masses are equal and located on the balance planes of the flow tubes. These forces, which are the subject of this invention, are generated when the masses affixed to the flow tubes have unequal moments of inertia about the lines connecting each respective tube's end nodes (hereafter referred to as bending axes).